The present invention relates to a digital information coding system for coding a bit train of binary digital information into a bit train suitable for use in digital recording, particularly for use in digital magnetic recording.
With coding methods suitable for high density digital recording, run length limited codes such as (2, 7) codes having a minimum run length of 2 (a minimum number of, e.g., "0s" inserted between "1" and "1") and a maximum run length of 7 (similarly, a maximum number of "0s"), (1, 7) codes having a minimum run length of 1 and a maximum run length of 7, and the like have been practically used.
Such coding methods are disclosed in particular, e.g., in Japanese Patent Laid-open Publications Nos. JP-A-55-47539, JP-A-58-13020, JP-A-58-119273 (corresponding to a U.S. Pat. No. 4,488,142) and the like.
The general characteristics such as channel capacity and the like of run length limited codes are described, e.g., in "IBM J. RES. DEVELOP.", Vol. 14, No. 4 (1970), pp. 376 to 383 and other publications.
The present invention seeks to provide the codes which have more generalized and extensive characteristics than those of already known run length limited codes. First, in order to clarify the problems associated with conventional run length limited codes, the characteristics of run length limited codes applied to digital magnetic recording will be described.
The characteristics of codes desired in digital magnetic recording are as follows:
(1) It is desired to have a large allowable value of time shift (which is called discrimination window width) between peak positions of reproduced signal pulses in order to discriminate codes of magnetically recorded digital signals. More particularly, in order to transform a usual code train without limitation of arrangement of "0" and "1" into another code train with limitation of arrangement such as run length limited codes, it becomes necessary to divide the original code train into blocks in units of m bits and transform each m bit block into an n bit code, where n is larger than m. The transformed digital code is magnetically recorded and reproduced. In this case, the data or code discrimination window width which is equal to the time occupied by one bit becomes m/n (which is represented by R) when the time length occupied by one bit of the original code is used as a time unit. For a desired characteristic, the value m/n should be as large as possible.
(2) It is desired to have a large minimum magnetization reversal distance in order to reduce interference between reproduced signal waveforms. Assuming that one magnetization reversal during recording occurs for each one transformed bit "1", the minimum magnetization reversal distance becomes d+1, where d is a minimum run length. The distance between adjacent "1s" becomes m/n.times.(d+1) (which is represented by R) when the time length occupied by one bit of the original code is used as a time unit. As the magnetization reversal distance between bits "1s" becomes larger, the interference between reproduced signal waveforms is more reduced so that it is desirable to have a larger value of m/n.times.(d+1).
The above-described characteristics (1) and (2) are illustrated in FIG. 4 with respect to conventionally used codes. In FIG. 4, the abscissa represents the discrimination timing window wodth W, i.e., m/n, and the ordinate represents the minimum magnetization reversal distance R, i.e., m/n.times.(d+1). The characteristic values as described with (1) and (2) are plotted relative to both the axes so that the desired characteristics are obtained at an upper right point in the graph. If a minimum run length is d, codes are plotted on a straight line with a gradient of d+1.
(2, 7) codes are represented at point 41 on a straight line with d=2, (1, 7) codes are represented at point 42 on a straight line width d=1, MFM codes are represented at point 43 on the straight line with d=1, and NRZ codes are represented at point 44 on a straight line with d=0.
It is necessary for a code with limitation of arrangement such as run length limited codes to satisfy the condition of m/n&lt;C, where C is a channel capacity. Therefore, the allowable maximum value of m/n is dependent on a given minimum run length d. Such maximum values are shown in FIG. 4 for each minimum run length d at points 45 on straight lines with a gradation of d+1, wherein the maximum run length k is assumed infinite and the value of the channel capacity C is indicated by the abscissa. The channel capacity C can be calculated by the following formula: ##EQU1## where (Sij) is a state transition matrix such as shown in FIG. 2 corresponding to a code state transition diagram such as shown in FIGS. 1A and 1B which are described later. If an element (ij) is 1, it means a transition from state i to state j, and if 0, it means that there is no transition.
The performance of high density recording is limited by and dependent on an inferior one of the two characteristics (1) and (2). Consider the conventionally utilized (2, 7) codes and (1, 7) codes. The discrimination window widths thereof are 0.5 and 0.667 and the minimum magnetization reversal distances thereof are 1.5 and 1.333, respectively. A factor of limiting high density recording of (2, 7) codes is that the discrimination window width thereof is small although a relatively large minimum magnetization reversal distance is possible. On the contrary, a factor of limiting high density recording of (1, 7) codes is that the minimum magnetization reversal distance thereof is small although a relatively large discrimination window width is possible. If there are such codes as having an intermediate characteristic between those of the (2, 7) and (1, 7) codes, such balanced characteristic will lead to high density recording.
As understood from FIG. 4, however, the run length limited codes are present only on the straight lines with a gradation d+1 (d=0, 1, 2, . . . ), and the codes located on an intermediate straight line are not found. In other words, since the value d is an integer, a gradient (d+1) of a straight line can not be set at an optional value. All other binary codes such as those conventionally known FM, PE, MFM codes, which have not been usually classified as falling into the category of run length limited codes, can be considered as a kind of run length limited codes so that they suffer the same restriction as described above.
It is convenient if the gradation can be varied substantially and optionally. For example, if an intermediate straight line between d=1 and d=2 can be obtained, a desired characteristic between both the characteristics (1) and (2) can be used.